The box model simulations were initialized using water vapour, ozone and CH4 measurements taken during the SEAC4RS aircraft campaign (more information on the chemical initialization is provided in Sect. ). It was based in Houston, Texas, and took place during August and September 2013 . One aim of this campaign was to investigate the impact of deep convective clouds on the water vapour content and the chemistry in the lowermost stratosphere. We initialized the model using measurements taken on 8 August 2013 by the Harvard Lyman-α photofragment fluorescence hygrometer HWV,, which flew on the NASA ER-2 high altitude research aircraft. Ozone was initialized in our simulations using O3 measurements from the National Oceanic and Atmospheric Administration (NOAA) UAS O3 instrument . Initial Cly and NOy were determined using tracer–tracer correlations (for more information see Sect. ) based on methane measurements with the Harvard University Picarro Cavity Ring down Spectrometer (HUPCRS) .

Diabatic trajectories were calculated using wind and temperature data from the ERA-Interim reanalysis with 1∘×1∘ resolution provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). The vertical velocities were calculated from the total diabatic heating rates derived from ERA-Interim data . Trajectories (7 d forward and backward) were initialized during SEAC4RS at locations where stratospheric water vapour was over 10 ppmv.

A selected example of calculated trajectories is shown in Fig. . This trajectory was chosen for the chemical analysis, because its initial conditions exhibited enhanced water vapour relative to the overall background, low temperatures and enhanced Cly (higher than for comparable water vapour and temperature conditions). Cly was calculated from tracer–tracer correlations (see Sect. ). This trajectory is then most suitable for the occurrence of the mechanism proposed by . In Fig. 1a, a backward trajectory is presented in the range of -7 to 0 d from the time of measurement (red line) and a forward trajectory in the range from 0 to 7 d. In Fig. 1b and c, the location of the measurement is shown by a red square.

The trajectories shown (Fig. , a forward and a backward trajectory) are based on measurements on 8 August 2013 during the SEAC4RS campaign. With a potential temperature of 380 to 390 K, these trajectories are above the tropopause of ∼366 K (Fig. a, grey line), deduced from the temperature profile measured during the flight. Both the forward and backward trajectories stay in the region of the North American continent.

For the SEAC4RS campaign, the temperature range of the backward trajectory varies between 197 and 202 K and the forward trajectory exhibits increasing temperatures. In addition, we considered trajectories based on other SEAC4RS measurements with enhanced water vapour; however, most of them exhibit higher mean temperatures of at least 200 K. Since low temperatures are expected to push stratospheric ozone depletion in mid-latitudes due to faster heterogeneous chemical reactions and thus faster chlorine activation, the SEAC4RS backward trajectory (Fig. , day -7 to 0) is selected here as the standard trajectory. This trajectory is used to analyse the chemical mechanisms affecting lower stratospheric ozone under various water vapour conditions, and to explore the sensitivity of these processes to different initial conditions.

Important trace gases for ozone chemistry – O3, Cly and NOy – are initialized based on measurements during the SEAC4RS aircraft campaign over North America (see Sect. ). Ozone and water vapour were measured directly during the aircraft campaign, and Cly and NOy are inferred from tracer–tracer correlations using CH4 measured on the aircraft employed. The initialization of all further trace gases except for water vapour were taken from the full chemistry 3D-CLaMS simulation for summer 2012 at the location of the measurement. Chemistry was initialized 7 d before the measurement. However, this time shift does not affect the sensitivities and the mechanism investigated here, because the trace gases Cly and NOy were initialized based on measured CH4 mixing ratios, which do not change significantly during a 7 d box-model simulation.

At water vapour mixing ratios up to 11.8 ppmv, net ozone formation occurs during the 7 d simulation (see Fig. ). This ozone formation is mainly driven by the photolysis of O2. Additionally the “Ozone Smog Cycle” known from tropospheric chemistry can yield ozone formation in the lower stratosphere . R4OH+CO⟶CO2+HR5H+O2+M⟶HO2+MR6HO2+NO⟶NO2+OHR7NO2+hν⟶NO+O(3P)R8O2+O(3P)+M⟶O3+M¯C1net: CO+2O2⟶CO2+O3 The rate of this cycle is determined by Reaction () at low water vapour mixing ratios, and its net reaction is the oxidation of CO. The ozone formation through this cycle contributes around 40 % to the total ozone formation at 5 ppmv in our box model standard simulation. Hence, the ozone formation which occurs in the simulations assuming low water vapour mixing ratios is due to both the photolysis of O2 and cycle (C1).

For higher water vapour mixing ratios than 12 ppmv, net ozone depletion is simulated (Fig. ) in the 7 d standard simulation. The ozone loss mechanism generally consists of two steps: a chlorine activation step transferring inactive chlorine (HCl) into active ClOx followed by catalytic ozone loss processes . We analyse both the chlorine activation step and subsequent catalytic ozone loss cycles potentially occurring in mid-latitudes in the lower stratosphere under enhanced water vapour conditions. Since ozone depletion is larger at high water vapour mixing ratios, conditions with a water vapour mixing ratio of 15 ppmv are chosen here to analyse the chemical ozone loss mechanism. Figure  shows an overview of the development of important mixing ratios and reaction rates during the 7 d simulation. Panel (a) illustrates temperature (black line) and surface area density of liquid particles (blue line).

The first phase of the ozone loss mechanism (dark grey background in Fig. ) is dominated by the occurrence of heterogeneous reactions. The most important heterogeneous chlorine activation reaction is Reaction () (Fig. b), which leads to the chlorine activation chain R9ClO+NO2+M⟶ClONO2+M,R1ClONO2+HCl⟶het.Cl2+HNO3,R10Cl2+hν⟶2Cl,R112×(Cl+O3⟶ClO+O2)¯,net: HCl+NO2+2O3⟶ClO+HNO3+2O2.

This chlorine activation chain yields a transformation of inactive HCl into active ClOx as well as of NOx into HNO3. The ozone loss due to this reaction chain is negligible and no depleting effect on ozone occurs during the first phase (Fig. c). In Fig. f, the NOx mixing ratio is seen to decrease and HNO3 increases due to Reaction (). Further, in the first phase the HCl mixing ratio decreases, yielding an increase in ClOx (Fig. f). Both decreasing NOx and increasing ClOx have an impact on ozone during the second phase of the ozone loss mechanism (light grey background in Fig. ), which is characterized by a decreasing ozone mixing ratio (Fig. c). The role of NOx and ClOx is discussed in detail in the next sections.

Modifying temperature, sulfate amount, or the mixing ratios of Cly or NOy yields a shift of the water vapour threshold. Figure  shows the ozone values reached at the end of the 7 d simulation (final ozone) for a variety of sensitivity cases assuming the standard trajectory. For each case, the water vapour threshold is marked with an arrow in the colour of the corresponding case.

The water-vapour-dependent final ozone values for the standard case are plotted as blue squares (Fig. ) with a water vapour threshold of 10.6 ppmv (see Sect. ). Raising the trajectory temperature by 1 K over the standard case leads to a higher water vapour threshold of 13.0 ppmv (open red squares), while increasing the sulfate content by a factor of 3 results in a lower threshold region of ∼ 9.0 ppmv (yellow diamonds). An even larger enhancement of the sulfate content (10× H2SO4, magenta diamonds) lowers the water vapour threshold further to a value near ∼ 8 ppmv. Reducing the NOy mixing ratio to 80 % of the standard case yields a shift of the threshold to a lower water vapour mixing ratio (green filled triangles), while an equivalent reduction in the Cly mixing ratio shifts the threshold to higher water vapour mixing ratios (black circles). A reduction in Cly also reduces ozone destruction and hence results in higher ozone mixing ratios at the end of the simulation. The sensitivity of the water vapour threshold to temperature, sulfate abundance, and the Cly and NOy mixing ratio is explained in the next section (Sect. ).

As a further example for an event with high stratospheric water vapour mixing ratios based on airborne measurements, simulations based on measurements during the Mid-latitude Airborne Cirrus Properties Experiments (MACPEX) were conducted. This campaign was based in Texas during springtime 2011 and hence prior to the formation of the North American Monsoon (NAM). A detailed description of this MACPEX case is given in Appendix . For the MACPEX case, changes in sulfate, Cly and NOy mixing ratios affect the water vapour threshold similarly to that observed for the SEAC4RS trajectory. Thus, the MACPEX results confirm the SEC4RS findings. Therefore, we conclude that in the considered temperature range (∼197–202 K), an ozone reduction occurs after exceeding a water vapour threshold and that this threshold varies with Cly, NOy, sulfate content and temperature.

The sensitivity of the water vapour threshold to Cly, NOy, sulfate loading and temperature is investigated, focussing on the balance between heterogeneous chlorine activation mainly due to Reaction () (ClONO2+HCl) and gas phase chlorine deactivation mainly due to Reaction (R12) (Cl+CH4). Net chlorine activation takes place when the chlorine activation rate exceeds the chlorine deactivation rate. Reaction () is the key reaction in the chlorine activation process. Therefore, in the following, first the dependence of Reaction () on the water vapour content is analysed in detail. Second, the balance between chlorine activation and deactivation is investigated, also considering the impact of Cly, NOy, sulfate and temperature on the water vapour threshold.

In general the rate of Reaction () (ClONO2+HCl) vR1 is determined through 1vR1=kR1⋅cClONO2⋅cHCl. The concentrations of ClONO2 cClONO2 and HCl cHCl are associated with the gas phase mixing ratio, and the rate constant kR1, as a measure of the reactivity of the heterogeneous reaction, depends in this case on the γ value γR1, the surface area of the liquid particle Aliq, the temperature T and cHCl (Eq. 2) . 2kR1∝γR1⋅Aliq⋅T1+cHCl The γ value describes the uptake of ClONO2 into liquid particles due to the decomposition of ClONO2 during Reaction () and is thus a measure of the probability of the occurrence of this heterogeneous reaction . Laboratory studies showed a dependence of γR1 on the solubility of HCl in the droplet, which generally increases for a lower H2SO4 fraction in the particle (H2SO4 wt %) . From Eq. (2) it is obvious that a large surface area Aliq and a high γ value γR1 increase kR1 and thus the heterogeneous reaction rate vR1.

In Fig. , the impact of the water vapour content on the H2SO4 weight percent, γR1, Aliq, kR1 and the reaction rate vR1 is shown. To avoid the influence of Reaction () itself on these parameters as much as possible, these parameters are selected for 1 August 2013 at 13:00 UTC. This point in time corresponds to the values after the first chemistry time step during the chemical simulation. The weight percent of H2SO4 in the particles decreases for all cases with increasing water vapour from more than 50 wt % at 5 ppmv H2O to around 20 wt % at 20 ppmv H2O due to an increasing uptake of H2O in the thermodynamic equilibrium. The standard case is illustrated in blue squares (Fig. ) and exhibits a strongly increasing gamma value especially for water vapour mixing ratios between 9 and 14 ppmv due to a lower H2SO4 wt %. In the same water vapour range, the liquid surface area density Aliq increases slightly. It increases more for higher water vapour mixing ratios because of HNO3 uptake into the particles. Due to the increasing γ value with increasing water vapour, the rate constant kR1 increases and thus induces a larger reaction rate vR1 with an increasing water vapour mixing ratio.

At low water vapour mixing ratios, not only the rate of Reaction () (ClONO2+HCl) but also that of Reaction (R12) (CH4+Cl) increases with increasing water content (Fig. f). An increasing heterogeneous reaction rate (Reaction ) results in both a lower NOx mixing ratio and more HCl converted into ClOx. A higher ClOx concentration yields a higher Cl mixing ratio and thus an increase in the rate of Reaction (R12) (CH4+Cl). Since both the rates of Reactions () and (R12) increase, no significant net chlorine activation occurs. Around the water vapour threshold, the Cl mixing ratio peaks (Fig. g), because less ClO is converted into Cl through R23ClO+NO⟶Cl+NO2 due to the decreasing NOx mixing ratio. The lower Cl mixing ratio reduces the HCl formation in Reaction (R12) (CH4+Cl). Hence, the increasing heterogeneous reactivity kR1 yields a higher rate of Reaction () and in the same way it impedes Reaction (R12) by reducing the NOx mixing ratio. As a consequence the rate of Reaction () exceeds the rate of Reaction (R12) and a net chlorine activation takes place, leading to a reduction in HCl. The decline in both HCl and NOx yields smaller rates of Reactions () and (R12) at high water amounts and thus a peak of Reactions () and (R12) (Fig. f). Hence, the increasing heterogeneous reactivity (kR1) of Reaction () destabilizes the balance between chlorine activation and deactivation by promoting the chlorine activation (due to an increasing rate of Reaction ) and impeding chlorine deactivation (due to a reduction of Reaction R12). This yields heterogeneous chlorine activation to exceed gas phase HCl formation in the water vapour threshold region.

For an enhanced sulfate content (Fig. , yellow diamonds), the particle surface area density (Aliq) is larger, leading to both a stronger increase in the heterogeneous reactivity (kR1) and hence a higher heterogeneous reaction rate than in the standard case. Due to this higher heterogeneous reactivity (kR1), the chlorine activation rate exceeds the chlorine deactivation at a lower water vapour mixing ratio and the net chlorine activation is reached at a lower water vapour threshold. A shift to higher temperatures (Fig. , red) yields almost no change in the surface area density (Aliq) but a reduced y value due to a higher H2SO4 fraction in the particles (H2SO4 wt %) and thus a lower heterogeneous reactivity (kR1). The reduced reactivity causes the net chlorine activation to occur at a higher water vapour threshold.

In contrast, the shift of the threshold for simulations with only 80 % of standard NOy (0.8 NOy; Fig. , green) or Cly (0.8 Cly; Fig. , black) can not be explained only by an increase in kR1. In these cases, further effects on the balance between chlorine activation and chlorine deactivation have to be taken into account. The water vapour threshold in the 0.8 NOy simulation (green triangles) is shifted to lower water vapour values due to a smaller Cl/ClO ratio for lower NOx concentrations. This yields a reduced HCl formation through Reaction (R12) (CH4+Cl) than in the standard case and thus impedes chlorine deactivation. The reduced chlorine deactivation affects the balance between chlorine activation and deactivation in a way that the water vapour threshold region in the 0.8 NOy case is lower than in the standard case. In the 0.8 Cly case (Fig. , black), the HCl and ClONO2 mixing ratios are reduced. This leads to a lower chlorine activation rate vR1 than in the standard case, despite the slight higher heterogeneous reactivity (kR1), which is due to the inverse dependence of kR1 on the HCl concentration (Eq. 2). The lower dependence of Reaction (R12) (Cl+CH4) than of Reaction () (HCl+ClONO2) on the Cly mixing ratio would push chlorine deactivation (Reaction R12) in the balance between chlorine activation and deactivation and hence shift the water vapour threshold to higher water vapour mixing ratios. Additionally caused by the lower rate of Reaction () (ClONO2+HCl) for reduced Cly, the NOx mixing ratio decreases more slowly. This enhances the rate of Reaction (R12) compared with the standard case as well, because more NOx yields a higher Cl/ClO ratio.

In summary, the water vapour threshold is determined by the balance between chlorine activation and deactivation and is thus in a certain temperature range especially sensitive to the water dependence of the heterogeneous reactivity (kR1), mainly described through the y value γR1 and the particle surface Aliq. These parameters are dependent on the present temperature and sulfate content. However, further parameters influencing this balance, such as the NOy and Cly mixing ratio, have an impact on the water vapour threshold as well.

The water vapour threshold, which has to be exceeded for chlorine activation and stratospheric ozone loss to occur, is mainly dependent on the temperature. To illustrate the impact of both temperature and water vapour mixing ratio on stratospheric ozone, the relative ozone change occurring after a 7 d simulation, in which a constant temperature and water vapour concentration and the Cly and NOy values of the standard case are assumed, is shown in Fig. . In panel (a), ozone change as a function of temperature and water vapour is plotted for non-enhanced sulfate amounts. In the right panel, the relative ozone change is shown for 10× standard sulfate to estimate a potential impact of volcanic eruptions or sulfate geoengineering on stratospheric ozone. Since mixing of neighbouring air parcels is neglected in the box-model study, the relative ozone change calculated corresponds to the largest possible ozone change for the conditions assumed. A mixing of moist tropospheric air with dry stratospheric air is expected to reduce the water vapour mixing ratio during the time period of the 7 d trajectory and hence could stop ozone depletion before the end of the trajectory is reached. In addition to the relative ozone change, the threshold for chlorine activation is shown as a white line in both panels. When temperature is held constant, this threshold corresponds to the water vapour threshold discussed above. Chlorine activation occurs at higher water mixing ratios and lower temperatures relative to the white line plotted. Here, chlorine is defined to be activated, if the ClOx/Cly ratio exceeds 10 %.

For climatological non-enhanced sulfate amounts (Fig. a), the temperature has to fall below 203 K for chlorine activation to occur, even for high water vapour mixing ratios of 20 ppmv. For the simultaneous presence of high water vapour and low temperatures an ozone loss of 9 % (max. 27 ppbv O3) was found. This maximal ozone loss occurs for a range of low temperatures (195–200 K) and enhanced water vapour mixing ratios (10–20 ppmv), because of a similar time until chlorine activation occurs. If the temperatures are higher and water vapour mixing ratios lower than the chlorine activation line, the ozone mixing ratio increases around 3.5 % (∼10 ppbv O3). At enhanced sulfate conditions (Fig. b) an ozone loss of max. 10 % (30 ppmv O3) occurs for low temperatures and high water vapour mixing ratios. For a water vapour mixing ratio of 20 ppmv the temperature has to fall below 205 K for ozone loss to occur. If the temperatures are very low (195–200 K) and the water vapour is high (10–20 ppmv) ozone loss is slightly reduced. This turnaround occurs, because at a high sulfate loading in combination with high water and low temperatures more HCl is taken up by condensed particles. This leads to less Cly in the gas phase and thus lower rates of catalytic ozone loss.

In summary, the combination of low temperatures, enhanced sulfate concentrations and high water vapour mixing ratios promotes an ozone decrease in up to ∼10 % (corresponding to maximum -30 ppbv O3). In comparison to the study of , the temperatures have to fall below 203 K (here) instead of 205 K (in ) for non-enhanced sulfate conditions, below 205 K instead of 208 K (in ) for enhanced sulfate conditions, and a water vapour mixing ratio of 20 ppmv for chlorine activation and thus ozone loss to occur. Hence, found ozone loss in mid-latitudes at high water vapour mixing ratios for temperatures 2 to 3 K higher than in our simulations.

The simulation of the case based on observations during the SEAC4RS aircraft campaign corresponds to the most realistic case for today's chemical conditions. It is identical to that of the standard case but assumes a fixed water vapour mixing ratio of 10.6 ppmv observed on 8 August 2013. Under these conditions, neither relevant heterogeneous chlorine activation due to Reaction () (ClONO2+HCl) nor catalytic ozone loss cycles (e.g. based on ClO+BrO) can be observed in the simulation (Fig. a). Instead, ozone is formed. In comparison, the same simulation with 0.6 ppbv gas phase equivalent H2SO4 instead of 0.2 ppbv was conducted (Fig. b). The enhanced sulfate content yields a larger liquid surface area density and thus an increased heterogeneous reactivity. Hence, Reaction () occurs in the 3×H2SO4 simulation significantly, leading to a slightly increasing ClOx mixing ratio and a decrease in the NOx mixing ratio. Both a reduced ozone formation in Cycle (C1) (which is at decreased NOx concentrations limited by Reaction ) and ozone loss cycles (e.g. based on the reaction ClO+BrO or ClO+HO2) can be observed, resulting in a reduction in ozone.

Using initial conditions, the trajectory corresponding to the SEAC4RS observations shows ozone loss with sulfate enhanced by a factor of 3. However, we note that this was an unusually cold trajectory. A more common case with higher mean temperatures would require a higher sulfate content to enhance the heterogeneous reactivity so that chlorine activation can occur. Thus under current chemical conditions in the UTLS (upper troposphere, lower stratosphere), it is most unlikely to get significant ozone loss by convectively injected water vapour in mid-latitudes.

Under conditions of substantially higher initial Cly and NOy mixing ratios (see Table ) than in the standard case used in , a larger ozone loss up to 265 ppbv during the 7 d simulation is simulated (Fig. a). Since these high-Cly conditions have been criticized in other studies e.g. as being unrealistically high, they are assumed here as a worst-case scenario. Under high chlorine conditions, and for a high water vapour content (more than ≈18 ppmv), an almost complete ozone destruction with a final ozone value of less than 50 ppbv is simulated (Fig. a), which corresponds to parcel ozone loss of 85 %. During the 3.5 d simulation in the study of , an ozone loss of 20 % with respect to initial ozone occurs for 18 ppmv H2O. This difference in relative ozone loss for similar conditions here and in the study of is caused by a longer assumed ozone destruction period in our simulation. Since the Cly mixing ratio is much higher than in the standard case, the catalytic ozone loss cycles are dominated by the ClO–dimer cycle (see Sect. S1 in the Supplements for chemical details). Assuming the measured water vapour content of 10.6 ppmv for high chlorine conditions would lead to an ozone depletion of 57 % during the 7 d simulation. In comparison, in the standard case an ozone loss of 8 % is reached when a high water vapour mixing ratio of 20 ppmv is assumed. However, even for the standard trajectory and a high chlorine content, a water vapour amount of 8 ppmv has to be exceeded to yield any ozone reduction. This threshold shifts from 8 ppmv to 7 ppmv for the case where stratospheric sulfate is tripled (Fig. a, yellow triangles).

The mixing ratio of inorganic bromine (Bry) has a high uncertainty in the lowermost stratosphere due to the influence of very short-lived bromine-containing substances. For example, during the CONTRAST field campaign (January–February 2014, western Pacific region), observed a Bry mixing ratio in the lower stratosphere of 5.6–7.3 pptv and the contribution of Bry, which crosses the tropopause, was estimated to be 2.1 ± 2.1 pptv . found somewhat different bromine partitioning depending on the ozone, NO2 and Cly concentrations, using very short-lived bromine species observations in the eastern and western Pacific ocean from the ATTREX campaign. Because our Bry values are not based on measurements for this specific case modelled, we tested the sensitivity to a value that is half of our standard case. The impact of this Bry reduction is illustrated in Fig. b.

Comparing the final ozone value for the 0.5 Bry simulations (Fig. b, light blue triangles) with those of the standard case (blue squares), a higher water vapour threshold and a reduced ozone loss of about 30 % at high water vapour mixing ratios are simulated. The shift of the water vapour threshold is due to the impact of Bry on the NO2/NO ratio. Due to the reaction R26BrO+NO⟶Br+NO2, reduced Bry yields a smaller NO2/NO ratio and hence less ClONO2 formation in Reaction () (ClO+NO2). Since ClONO2 formation is essential for chlorine activation in Reaction () (ClONO2+HCl), reduced Bry yields a lower chlorine activation rate and thus a shift of the water vapour threshold to higher water vapour mixing ratios. In the case of reduced Bry, less ozone is destroyed regarding the standard case. The ozone destruction in the ClO–BrO cycle is reduced, while the rates of Reaction () (ClO+ClO) and Reaction () (ClO+HO2) are similar to those of the standard case (Fig. e; for chemical details of the reduced-Bry case see Sect. S2). This results in the reduced ozone destruction in the 0.5 Bry case.

Since the occurrence of the ozone loss process analysed in this study is strongly dependent on a variety of parameters, the time period over which the ozone loss might occur is very uncertain. The impact of this time period on ozone loss was tested by extending the 7 d trajectory used in the sections above to span the entire period with temperatures low enough to maintain chlorine activation. In this time-extended simulation, temperatures are well below 200 K at the beginning of the simulation and remain below 201 K for 14 d. Hence, chlorine activation can be maintained for a longer time period than in the standard case and breaks up due to increasing temperatures (for details regarding chemical processes and temperature development along the extended trajectory see Sect. S3).

Because of the extended time period, the final ozone values using the enhanced water vapour mixing ratios for the longer trajectory (cyan triangles Fig. c) are much lower than those of the standard 7 d simulation (blue squares). Additionally, more ozone is formed when using low water vapour concentrations. Comparing the water vapour threshold of the 7 d trajectory (∼10.6 ppmv) and the 19 d simulation (10.2 ppmv), a shift to lower water vapour mixing ratios occurs in the 19 d trajectory. This shift is likely due to an extended time period with a temperature well below 200 K at the beginning of this trajectory, which allows a chlorine activation to occur even for slightly lower water vapour amounts. Simulations along a trajectory starting on the same day as the 7 d trajectory, but finishing on 15 August, yield the same water vapour threshold as the 7 d simulation (not shown), indicating that the shift in the threshold shown in Fig.  is associated with the very cold conditions at the start of the 19 d simulation. Hence, the length of the chosen trajectory has no impact on the water vapour threshold but does affect the final ozone.